Precise Measurement of the D0 and D+ Lifetimes at Belle II

Precise Measurement of the D

⁰

and D

⁺

Lifetimes at Belle II

F. Abudin´en,³¹I. Adachi,^21,18K. Adamczyk,⁶⁶L. Aggarwal,⁷³H. Ahmed,⁷⁶H. Aihara,¹¹²N. Akopov,² A. Aloisio,^88,25 N. Anh Ky,^40,13D. M. Asner,³H. Atmacan,⁹⁹V. Aushev,⁸¹V. Babu,¹¹S. Bacher,⁶⁶H. Bae,¹¹²S. Baehr,⁴⁶S. Bahinipati,³³ P. Bambade,⁹⁵Sw. Banerjee,¹⁰³S. Bansal,⁷³M. Barrett,²¹J. Baudot,⁹⁶M. Bauer,⁴⁶A. Baur,¹¹J. Becker,⁴⁶P. K. Behera,³⁵

J. V. Bennett,¹⁰⁶ E. Bernieri,²⁹F. U. Bernlochner,⁹⁷M. Bertemes,³⁸E. Bertholet,⁸⁴M. Bessner,¹⁰¹ S. Bettarini,^91,28 V. Bhardwaj,³²F. Bianchi,^93,30T. Bilka,⁷S. Bilokin,⁵⁴ D. Biswas,¹⁰³ A. Bobrov,^4,68D. Bodrov,^64,52A. Bolz,¹¹ A. Bozek,⁶⁶ M. Bračko,^104,80 P. Branchini,²⁹N. Braun,⁴⁶R. A. Briere,⁵ T. E. Browder,¹⁰¹ A. Budano,²⁹S. Bussino,^92,29 M. Campajola,^88,25L. Cao,¹¹G. Casarosa,^91,28 C. Cecchi,^90,27D. Červenkov,⁷ M.-C. Chang,¹⁵P. Chang,⁶⁵R. Cheaib,¹¹

V. Chekelian,⁵⁷C. Chen,⁴²Y.-T. Chen,⁶⁵B. G. Cheon,²⁰K. Chilikin,⁵² K. Chirapatpimol,⁸ H.-E. Cho,²⁰ K. Cho,⁴⁸ S.-J. Cho,¹¹⁸S.-K. Choi,¹⁹S. Choudhury,³⁴D. Cinabro,¹¹⁶L. Corona,^91,28L. M. Cremaldi,¹⁰⁶S. Cunliffe,¹¹T. Czank,¹¹³ F. Dattola,¹¹E. De La Cruz-Burelo,⁶G. de Marino,⁹⁵G. De Nardo,^88,25G. De Pietro,²⁹R. de Sangro,²⁴M. Destefanis,^93,30 S. Dey,⁸⁴A. De Yta-Hernandez,⁶A. Di Canto ,³F. Di Capua,^88,25J. Dingfelder,⁹⁷Z. Doležal,⁷I. Domínguez Jim´enez,⁸⁷ T. V. Dong,¹³M. Dorigo,³¹K. Dort,⁴⁵D. Dossett,¹⁰⁵S. Dubey,¹⁰¹S. Duell,⁹⁷G. Dujany,⁹⁶P. Ecker,⁴⁶D. Epifanov,^4,68 T. Ferber,¹¹D. Ferlewicz,¹⁰⁵G. Finocchiaro,²⁴K. Flood,¹⁰¹A. Fodor,⁵⁸ F. Forti,^91,28 B. G. Fulsom,⁷²A. Gabrielli,^94,31

N. Gabyshev,^4,68A. Gaz,^89,26A. Gellrich,¹¹G. Giakoustidis,⁹⁷R. Giordano,^88,25A. Giri,³⁴A. Glazov,¹¹B. Gobbo,³¹ R. Godang,¹¹⁰P. Goldenzweig,⁴⁶B. Golob,^102,80 W. Gradl,⁴⁴E. Graziani,²⁹D. Greenwald,⁸³T. Gu,¹⁰⁸ Y. Guan,⁹⁹ K. Gudkova,^4,68J. Guilliams,¹⁰⁶C. Hadjivasiliou,⁷²S. Halder,⁸²K. Hara,^21,18T. Hara,^21,18O. Hartbrich,¹⁰¹K. Hayasaka,⁶⁷

H. Hayashii,⁶³ S. Hazra,⁸²C. Hearty,^98,39I. Heredia de la Cruz,^6,10M. Hernández Villanueva,¹¹A. Hershenhorn,⁹⁸ T. Higuchi,¹¹³E. C. Hill,⁹⁸H. Hirata,⁶⁰M. Hoek,⁴⁴M. Hohmann,¹⁰⁵C.-L. Hsu,¹¹¹T. Humair,⁵⁷T. Iijima,^60,62K. Inami,⁶⁰ G. Inguglia,³⁸A. Ishikawa,^21,18R. Itoh,^21,18M. Iwasaki,⁷⁰Y. Iwasaki,²¹W. W. Jacobs,³⁶D. E. Jaffe,³E.-J. Jang,¹⁹S. Jia,¹⁶ Y. Jin,³¹H. Junkerkalefeld,⁹⁷H. Kakuno,⁸⁶A. B. Kaliyar,⁸²J. Kandra,⁷K. H. Kang,⁵¹R. Karl,¹¹G. Karyan,²Y. Kato,^60,62

T. Kawasaki,⁴⁷C. Kiesling,⁵⁷C.-H. Kim,²⁰D. Y. Kim,⁷⁹Y.-K. Kim,¹¹⁸Y. Kim,⁴⁹ T. D. Kimmel,¹¹⁵K. Kinoshita,⁹⁹ P. Kodyš,⁷ T. Koga,²¹S. Kohani,¹⁰¹T. Konno,⁴⁷ S. Korpar,^104,80 E. Kovalenko,^4,68R. Kowalewski,¹¹⁴T. M.

G. Kraetzschmar,⁵⁷F. Krinner,⁵⁷P. Križan,^102,80P. Krokovny,^4,68T. Kuhr,⁵⁴J. Kumar,⁵ M. Kumar,⁵⁶R. Kumar,⁷⁴ K. Kumara,¹¹⁶S. Kurz,¹¹A. Kuzmin,^4,68Y.-J. Kwon,¹¹⁸S. Lacaprara,²⁶K. Lalwani,⁵⁶T. Lam,¹¹⁵L. Lanceri,³¹J. S. Lange,⁴⁵ M. Laurenza,^92,29K. Lautenbach,¹ F. R. Le Diberder,⁹⁵S. C. Lee,⁵¹P. Leitl,⁵⁷D. Levit,⁸³C. Li,⁵³L. K. Li,⁹⁹J. Libby,³⁵ K. Lieret,⁵⁴Z. Liptak,²³Q. Y. Liu,¹¹D. Liventsev,^116,21S. Longo,¹¹T. Lueck,⁵⁴C. Lyu,⁹⁷R. Manfredi,^94,31E. Manoni,²⁷ C. Marinas,⁴¹A. Martini,¹¹T. Matsuda,¹⁰⁷K. Matsuoka,²¹D. Matvienko,^4,52,68J. A. McKenna,⁹⁸F. Meier,¹²M. Merola,^88,25

F. Metzner,⁴⁶C. Miller,¹¹⁴ K. Miyabayashi,⁶³R. Mizuk,^52,64G. B. Mohanty,⁸²N. Molina-Gonzalez,⁶ H. Moon,⁴⁹ H.-G. Moser,⁵⁷M. Mrvar,³⁸C. Murphy,¹¹³R. Mussa,³⁰I. Nakamura,^21,18 K. R. Nakamura,^21,18M. Nakao,^21,18 H. Nakazawa,⁶⁵Z. Natkaniec,⁶⁶A. Natochii,¹⁰¹G. Nazaryan,² C. Niebuhr,¹¹M. Niiyama,⁵⁰N. K. Nisar,³S. Nishida,^21,18

K. Nishimura,¹⁰¹S. Ogawa,⁸⁵Y. Onishchuk,⁸¹H. Ono,⁶⁷Y. Onuki,¹¹² P. Oskin,⁵²E. R. Oxford,⁵ H. Ozaki,^21,18 P. Pakhlov,^52,59A. Paladino,^91,28T. Pang,¹⁰⁸A. Panta,¹⁰⁶E. Paoloni,^91,28S. Pardi,²⁵H. Park,⁵¹S.-H. Park,²¹B. Paschen,⁹⁷

A. Passeri,²⁹A. Pathak,¹⁰³S. Patra,³²S. Paul,⁸³T. K. Pedlar,⁵⁵I. Peruzzi,²⁴R. Peschke,¹⁰¹R. Pestotnik,⁸⁰F. Pham,¹⁰⁵ M. Piccolo,²⁴L. E. Piilonen,¹¹⁵G. Pinna Angioni,^93,30P. L. M. Podesta-Lerma,⁸⁷T. Podobnik,⁸⁰S. Pokharel,¹⁰⁶G. Polat,¹

V. Popov,⁶⁴C. Praz,¹¹S. Prell,⁴²E. Prencipe,⁴⁵M. T. Prim,⁹⁷M. V. Purohit,⁶⁹H. Purwar,¹⁰¹ N. Rad,¹¹ P. Rados,³⁸ S. Raiz,^94,31 S. Reiter,⁴⁵M. Remnev,^4,68I. Ripp-Baudot,⁹⁶ G. Rizzo,^91,28L. B. Rizzuto,⁸⁰S. H. Robertson,^58,39 J. M. Roney,^114,39 A. Rostomyan,¹¹N. Rout,³⁵M. Rozanska,⁶⁶D. Sahoo,⁴²D. A. Sanders,¹⁰⁶S. Sandilya,³⁴A. Sangal,⁹⁹

L. Santelj,^102,80Y. Sato,²¹V. Savinov,¹⁰⁸ B. Scavino,⁴⁴J. Schueler,¹⁰¹ C. Schwanda,³⁸A. J. Schwartz,⁹⁹Y. Seino,⁶⁷ A. Selce,^29,14K. Senyo,¹¹⁷ J. Serrano,¹ C. Sfienti,⁴⁴J.-G. Shiu,⁶⁵B. Shwartz,^4,68A. Sibidanov,¹⁰¹ F. Simon,⁵⁷ R. J. Sobie,^114,39 A. Soffer,⁸⁴A. Sokolov,³⁷E. Solovieva,⁵²S. Spataro,^93,30 B. Spruck,⁴⁴M. Starič,⁸⁰ S. Stefkova,¹¹ Z. S. Stottler,¹¹⁵R. Stroili,^89,26J. Strube,⁷²M. Sumihama,^17,71W. Sutcliffe,⁹⁷S. Y. Suzuki,^21,18H. Svidras,¹¹M. Tabata,⁹ M. Takizawa,^75,22,77U. Tamponi,³⁰S. Tanaka,^21,18K. Tanida,⁴³H. Tanigawa,¹¹²N. Taniguchi,²¹F. Tenchini,^91,28R. Tiwary,⁸² D. Tonelli,³¹E. Torassa,²⁶N. Toutounji,¹¹¹ K. Trabelsi,⁹⁵T. Tsuboyama,^21,18I. Ueda,^21,18S. Uehara,^21,18Y. Uematsu,¹¹² T. Uglov,^52,64K. Unger,⁴⁶Y. Unno,²⁰K. Uno,⁶⁷S. Uno,^21,18P. Urquijo,¹⁰⁵Y. Ushiroda,^21,18,112Y. V. Usov,^4,68S. E. Vahsen,¹⁰¹ R. van Tonder,⁹⁷G. S. Varner,¹⁰¹A. Vinokurova,^4,68L. Vitale,^94,31A. Vossen,¹²E. Waheed,²¹H. M. Wakeling,⁵⁸E. Wang,¹⁰⁸ M.-Z. Wang,⁶⁵X. L. Wang,¹⁶A. Warburton,⁵⁸M. Watanabe,⁶⁷M. Welsch,⁹⁷C. Wessel,⁹⁷J. Wiechczynski,⁶⁶E. Won,⁴⁹ X. P. Xu,⁷⁸B. D. Yabsley,¹¹¹S. Yamada,²¹W. Yan,¹⁰⁹ S. B. Yang,⁴⁹H. Ye,¹¹J. Yelton,¹⁰⁰J. H. Yin,⁴⁹K. Yoshihara,⁶⁰

Y. Yusa,⁶⁷L. Zani,¹ V. Zhilich,^4,68 Q. D. Zhou,^60,61,62X. Y. Zhou,⁵³V. I. Zhukova,⁵²and R. Žlebčík⁷

(Belle II Collaboration)

1Aix Marseille Universit´e, CNRS/IN2P3, CPPM, 13288 Marseille, France

2Alikhanyan National Science Laboratory, Yerevan 0036, Armenia

3Brookhaven National Laboratory, Upton, New York 11973, USA

4Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090, Russian Federation

5Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

6Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional, Mexico City 07360, Mexico

7Faculty of Mathematics and Physics, Charles University, 121 16 Prague, Czech Republic

8Chiang Mai University, Chiang Mai 50202, Thailand

9Chiba University, Chiba 263-8522, Japan

10Consejo Nacional de Ciencia y Tecnología, Mexico City 03940, Mexico

11Deutsches Elektronen-Synchrotron, 22607 Hamburg, Germany

12Duke University, Durham, North Carolina 27708, USA

13Institute of Theoretical and Applied Research (ITAR), Duy Tan University, Hanoi 100000, Vietnam

14ENEA Casaccia, I-00123 Roma, Italy

15Department of Physics, Fu Jen Catholic University, Taipei 24205, Taiwan

16Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and Institute of Modern Physics, Fudan University, Shanghai 200443, China

17Gifu University, Gifu 501-1193, Japan

18The Graduate University for Advanced Studies (SOKENDAI), Hayama 240-0193, Japan

19Gyeongsang National University, Jinju 52828, South Korea

20Department of Physics and Institute of Natural Sciences, Hanyang University, Seoul 04763, South Korea

21High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan

22J-PARC Branch, KEK Theory Center, High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan

23Hiroshima University, Higashi-Hiroshima, Hiroshima 739-8530, Japan

24INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy

25INFN Sezione di Napoli, I-80126 Napoli, Italy

26INFN Sezione di Padova, I-35131 Padova, Italy

27INFN Sezione di Perugia, I-06123 Perugia, Italy

28INFN Sezione di Pisa, I-56127 Pisa, Italy

29INFN Sezione di Roma Tre, I-00146 Roma, Italy

30INFN Sezione di Torino, I-10125 Torino, Italy

31INFN Sezione di Trieste, I-34127 Trieste, Italy

32Indian Institute of Science Education and Research Mohali, SAS Nagar, 140306, India

33Indian Institute of Technology Bhubaneswar, Satya Nagar 751007, India

34Indian Institute of Technology Hyderabad, Telangana 502285, India

35Indian Institute of Technology Madras, Chennai 600036, India

36Indiana University, Bloomington, Indiana 47408, USA

37Institute for High Energy Physics, Protvino 142281, Russian Federation

38Institute of High Energy Physics, Vienna 1050, Austria

39Institute of Particle Physics (Canada), Victoria, British Columbia V8W 2Y2, Canada

40Institute of Physics, Vietnam Academy of Science and Technology (VAST), Hanoi, Vietnam

41Instituto de Fisica Corpuscular, Paterna 46980, Spain

42Iowa State University, Ames, Iowa 50011, USA

43Advanced Science Research Center, Japan Atomic Energy Agency, Naka 319-1195, Japan

44Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany

45Justus-Liebig-Universität Gießen, 35392 Gießen, Germany

46Institut für Experimentelle Teilchenphysik, Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany

47Kitasato University, Sagamihara 252-0373, Japan

48Korea Institute of Science and Technology Information, Daejeon 34141, South Korea

49Korea University, Seoul 02841, South Korea

50Kyoto Sangyo University, Kyoto 603-8555, Japan

51Kyungpook National University, Daegu 41566, South Korea

52P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow 119991, Russian Federation

53Liaoning Normal University, Dalian 116029, China

54Ludwig Maximilians University, 80539 Munich, Germany

55Luther College, Decorah, Iowa 52101, USA

56Malaviya National Institute of Technology Jaipur, Jaipur 302017, India

58McGill University, Montr´eal, Qu´ebec, H3A 2T8, Canada

59Moscow Physical Engineering Institute, Moscow 115409, Russian Federation

60Graduate School of Science, Nagoya University, Nagoya 464-8602, Japan

61Institute for Advanced Research, Nagoya University, Nagoya 464-8602, Japan

62Kobayashi-Maskawa Institute, Nagoya University, Nagoya 464-8602, Japan

63Nara Women’s University, Nara 630-8506, Japan

64National Research University Higher School of Economics, Moscow 101000, Russian Federation

65Department of Physics, National Taiwan University, Taipei 10617, Taiwan

66H. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342, Poland

67Niigata University, Niigata 950-2181, Japan

68Novosibirsk State University, Novosibirsk 630090, Russian Federation

69Okinawa Institute of Science and Technology, Okinawa 904-0495, Japan

70Osaka City University, Osaka 558-8585, Japan

71Research Center for Nuclear Physics, Osaka University, Osaka 567-0047, Japan

72Pacific Northwest National Laboratory, Richland, Washington, D.C. 99352, USA

73Panjab University, Chandigarh 160014, India

74Punjab Agricultural University, Ludhiana 141004, India

75Meson Science Laboratory, Cluster for Pioneering Research, RIKEN, Saitama 351-0198, Japan

76St. Francis Xavier University, Antigonish, Nova Scotia, B2G 2W5, Canada

77Showa Pharmaceutical University, Tokyo 194-8543, Japan

78Soochow University, Suzhou 215006, China

79Soongsil University, Seoul 06978, South Korea

80J. Stefan Institute, 1000 Ljubljana, Slovenia

81Taras Shevchenko National Univ. of Kiev, Kiev, Ukraine

82Tata Institute of Fundamental Research, Mumbai 400005, India

83Department of Physics, Technische Universität München, 85748 Garching, Germany

84Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel

85Toho University, Funabashi 274-8510, Japan

86Tokyo Metropolitan University, Tokyo 192-0397, Japan

87Universidad Autonoma de Sinaloa, Sinaloa 80000, Mexico

88Dipartimento di Scienze Fisiche, Universit `a di Napoli Federico II, I-80126 Napoli, Italy

89Dipartimento di Fisica e Astronomia, Universit `a di Padova, I-35131 Padova, Italy

90Dipartimento di Fisica, Universit `a di Perugia, I-06123 Perugia, Italy

91Dipartimento di Fisica, Universit `a di Pisa, I-56127 Pisa, Italy

92Dipartimento di Matematica e Fisica, Universit `a di Roma Tre, I-00146 Roma, Italy

93Dipartimento di Fisica, Universit `a di Torino, I-10125 Torino, Italy

94Dipartimento di Fisica, Universit `a di Trieste, I-34127 Trieste, Italy

95Universit´e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France

96Universit´e de Strasbourg, CNRS, IPHC, UMR 7178, 67037 Strasbourg, France

97University of Bonn, 53115 Bonn, Germany

98University of British Columbia, Vancouver, British Columbia, V6T 1Z1, Canada

99University of Cincinnati, Cincinnati, Ohio 45221, USA

100University of Florida, Gainesville, Florida 32611, USA

101University of Hawaii, Honolulu, Hawaii 96822, USA

102Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia

103University of Louisville, Louisville, Kentucky 40292, USA

104Faculty of Chemistry and Chemical Engineering, University of Maribor, 2000 Maribor, Slovenia

105School of Physics, University of Melbourne, Victoria 3010, Australia

106University of Mississippi, University, Mississippi 38677, USA

107University of Miyazaki, Miyazaki 889-2192, Japan

108University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA

109University of Science and Technology of China, Hefei 230026, China

110University of South Alabama, Mobile, Alabama 36688, USA

111School of Physics, University of Sydney, New South Wales 2006, Australia

112Department of Physics, University of Tokyo, Tokyo 113-0033, Japan

113Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa 277-8583, Japan

114University of Victoria, Victoria, British Columbia, V8W 3P6, Canada

115Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA

116Wayne State University, Detroit, Michigan 48202, USA

117Yamagata University, Yamagata 990-8560, Japan

118Yonsei University, Seoul 03722, South Korea

(Received 6 August 2021; accepted 20 October 2021; published 19 November 2021) We report a measurement of theD⁰andD^þlifetimes usingD⁰→K⁻π^þandD^þ→K⁻π^þπ^þdecays reconstructed ine^þe⁻→c¯c data recorded by the Belle II experiment at the SuperKEKB asymmetric- energy e^þe⁻ collider. The data, collected at center-of-mass energies at or near the ϒð4SÞ resonance, correspond to an integrated luminosity of72 fb⁻¹. The results,τðD⁰Þ ¼410.51.1ðstatÞ 0.8ðsystÞfs and τðD^þÞ ¼1030.44.7ðstatÞ 3.1ðsystÞfs, are the most precise to date and are consistent with previous determinations.

DOI:10.1103/PhysRevLett.127.211801

Accurate predictions of lifetimes of weakly decaying charmed and bottom hadrons are challenging because they involve strong-interaction theory at low energy. Predictions must resort to effective models, such as the heavy-quark expansion [1–6], which also underpin strong-interaction calculations required for the determination of fundamental standard-model parameters from hadron-decay measure- ments (e.g., to extract the strength of quark-mixing cou- plings from decay widths). Precise lifetime measurements provide excellent tests of such effective models. Lifetimes are also important inputs for a wide variety of studies because they are needed to compare measured decay branching fractions to predictions for partial decay widths.

Weakly decaying charmed hadrons have lifetimes rang- ing from about 0.1 to 1 ps[7]. The world averages of theD⁰ andD^þ lifetimes,410.11.5and10407fs, are almost exclusively determined from systematically limited per- mille-precision measurements made by FOCUS two dec- ades ago[7,8]. Recently, the LHCb Collaboration precisely measured the lifetimes of the D^þ_s meson and charmed baryons relative to that of the D^þ meson [9–12]. Such relative measurements minimize systematic uncertainties due to decay-time-biasing event-selection criteria that are particularly severe at hadron colliders. By contrast, experi- ments at e^þe⁻ colliders, owing to the reconstruction of large charmed hadron yields without decay-time-biasing selections, have a great potential for absolute lifetime measurements. With the first layer of its vertex detector only 1.4 cm away from the interaction region, the Belle II experiment at the SuperKEKB asymmetric-energy e^þe⁻ collider[13,14]obtains a decay-time resolution two times better than the Belle and BABARexperiments [15], ena- bling high precision for the measurement of charmed lifetimes with early data. To limit systematic uncertainties this potential must be complemented with an accurate

vertex-detector alignment, a precise calibration of final-state particle momenta, and powerful background discrimination.

In this Letter, we report high-precision measurements of the D⁰ and D^þ lifetimes using D^þ →D⁰ð→K⁻π^þÞπ^þ and D^þ→D^þð→K⁻π^þπ^þÞπ⁰ decays reconstructed in the data collected by Belle II during 2019 and the first half of 2020 at center-of-mass energies at or near the ϒð4SÞ resonance. (Charge-conjugate decays are implied through- out.) The data correspond to an integrated luminosity of 72fb⁻¹. At Belle II,D^þ mesons frome^þe⁻ →cc¯ events are produced with boosts that displace the D⁰ and D^þ decay points from those of production by approximately 200 and500μm on average, respectively. The decay time is measured from this displacement L⃗ , projected onto the direction of the momentump⃗ ast¼m_DL⃗ ·p=j⃗ pj⃗ ², where m_D is the known mass of the relevant D meson[7]. The decay-time uncertainty σ_t is calculated by propagating the uncertainties inL⃗ and ⃗p, including their correlations.

The lifetimes are measured using a fit to the ðt;σtÞ distributions of the reconstructed decay candidates. The sample selection and fit strategy have been optimized and validated using simulation; however, no input from simu- lation is used in the fit to data. To avoid bias, we inspected the lifetimes measured with the full data sample only after the entire analysis procedure was finalized and all uncertainties were determined. However, we examined the results from the subset of data collected during 2019 (approximately 13%

of the total) before the analysis was complete.

The Belle II detector[13]consists of several subsystems arranged in a cylindrical structure around the beam pipe.

The tracking system consists of a two-layer silicon-pixel detector (PXD), surrounded by a four-layer double-sided silicon-strip detector (SVD) and a 56-layer central drift chamber (CDC). Only two out of 12 ladders were installed in the second layer of the PXD for this data sample. The combined PXD and SVD system provides average decay- time resolutions of about 70 and 60 fs, respectively, for the D⁰andD^þdecays considered here. A time-of-propagation counter and an aerogel ring-imaging Cherenkov counter that cover the barrel and forward end cap regions of the Published by the American Physical Society under the terms of

the Creative Commons Attribution 4.0 International license.

Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

detector, respectively, are essential for charged-particle identification. The electromagnetic calorimeter fills the remaining volume inside a 1.5 T superconducting solenoid and serves to reconstruct photons and electrons. A dedi- cated system to identifyK⁰_Lmesons and muons is installed in the outermost part of the detector. The z axis of the laboratory frame is defined as the central axis of the solenoid, with its positive direction determined by the direction of the electron beam.

The simulation uses KKMC [16] to generate quark- antiquark pairs from e^þe⁻ collisions, PYTHIA8 [17] for hadronization,EVTGEN[18]for the decay of the generated hadrons, and GEANT4 [19]for the detector response.

The reconstruction [20–22] and selection of the signal candidates avoid any requirement that could bias the decay time or introduce a variation of the efficiency as a function of decay time, as checked in simulation. Events are first selected by vetoing events consistent with Bhabha scatter- ing and by requiring at least three tracks with loose upper bounds on their impact parameters and with transverse momenta greater than200MeV=c. These three tracks are not necessarily associated with the decay modes being reconstructed.

CandidateD⁰→K⁻π^þdecays are formed using pairs of oppositely charged tracks. Each track must have a hit in the first layer of the PXD, at least one hit in the SVD, at least 20 hits in the CDC, and be identified as a kaon, if negative, or else a pion. Low-momentum pion candidates are tracks consistent with originating from the interaction region that are required to have hits both in the SVD and CDC. They are combined with D⁰ candidates to form D^þ→D⁰π^þ decays. A global decay-chain vertex fit[23]constrains the tracks according to the decay topology and constrains the D^þ candidate to originate from the measured position of thee^þe⁻ interaction region (IR). Only candidates with fit χ² probabilities larger than 0.01 are retained for further analysis. The IR has typical dimensions of250μm along thezaxis and of 10 and0.3 μm in the two directions of the transverse plane. Its position and size vary over data taking and are regularly measured using e^þe⁻→μ^þμ⁻ events.

The mass of the D⁰ candidate mðK⁻π^þÞ must be in the range ½1.75;2.00GeV=c². The difference between the D^þ andD⁰ candidate massesΔm must satisfy144.94<

Δm <145.90 MeV=c² (3 times the Δm resolution around the signal peak). Since the D⁰ is assumed to originate from the IR, charmed mesons originating from displaced decays of bottom mesons would bias the lifetime measurement. They are suppressed to a negligible rate by requiring that the momentum of the D^þ in the e^þe⁻ center-of-mass system exceeds2.5GeV=c. After requiring 1.851< mðK⁻π^þÞ<1.878GeV=c² (signal region), multiple D^þ candidates occur in a few per mille of the selected events. In such events, one randomly selected candidate is retained for subsequent analysis.

The signal region contains approximately 171×10³ candidates with a signal purity of about 99.8%, as deter- mined from a binned least-squares fit to the mðK⁻π^þÞ distribution (Fig. 1). In the fit, the D⁰→K⁻π^þ signal is modeled with the sum of two Gaussian distributions and a Crystal Ball function [24]; misidentified decays of D⁰→ π^þπ⁻andD⁰→K^þK⁻, each modeled with a Johnson’sSU

distribution [25] with parameters determined from simu- lation, do not enter the signal region; the remaining background, modeled with an exponential distribution, is dominated by candidates formed by random combinations of particles.

The selection of the D^þ→D^þð→K⁻π^þπ^þÞπ⁰ candi- dates follows similar criteria to those for theD⁰mode, but with more stringent requirements to suppress a larger background contamination. Tracks identified as kaons or pions are required to have a hit in the first layer of the PXD, at least one hit in the SVD, and at least 30 hits in the CDC.

They are combined to formD^þ→K⁻π^þπ^þcandidates. To suppress backgrounds from misreconstructed charmed- hadron decays, such as four-body hadronic or semileptonic decays, the lower-momentum pion must have momentum exceeding 350MeV=c and the higher-momentum pion must not be identified as a lepton. Candidate π⁰→γγ decays are reconstructed using photon candidates from calorimetric energy clusters that are not associated with a track. Each photon energy must be larger than 80, 30, or 60 MeV if detected in the forward, central, or backward region, respectively, of the calorimeter. Neutral-pion can- didates with masses in the range ½120;145 MeV=c² and

1.75 1.8 1.85 1.9 1.95 2

2] Mass [GeV/c 102

103

104

1 10 102

103

104 Belle II = 72 fb1

L dt

Data Fit

Background K

0 K D D0 2cCandidates per 1 MeV/

FIG. 1. Mass distributions of (top)D⁰→K⁻π^þand (bottom) D^þ→K⁻π^þπ^þ candidates with fit projections overlaid. The vertical dashed and (for the bottom plot) dotted lines indicate the signal regions and the sideband, respectively.

momenta larger than 150MeV=c are combined withD^þ candidates to form D^þ→D^þπ⁰ decays. The D^þ decay chain is fit using IR andπ⁰mass constraints. Only candidates with fit χ²probabilities larger than 0.01 are retained. The mass of theD^þcandidate,mðK⁻π^þπ^þÞ, must be in the range

½1.75;2.00 GeV=c² and the difference between the D^þ andD^þmasses in the range½138;143 MeV=c²(3times theΔmresolution around the signal peak). The momentum of theD^þin thee^þe⁻center-of-mass system must exceed 2.6GeV=cto suppressD^þ candidates from bottom mes- ons. This requirement is tighter than that used for D⁰ candidates because of the less-precise π⁰ -momentum resolution.

The signal region in mðK⁻π^þπ^þÞ is defined as

½1.855;1.883GeV=c² (Fig.1). It contains approximately 59×10³ candidates after randomly selecting one D^þ candidate for the percent-level fraction of events where more than one is found. A binned least-squares fit to the mðK⁻π^þπ^þÞdistribution identifies about 9% of candidates in the signal region as background. Simulation shows that such background is composed of misreconstructed charmed decays and random track combinations. In the fit, theD^þ →K⁻π^þπ^þ signal is modeled with the sum of two Gaussian distributions and a Crystal Ball function; the background is modeled with an exponential distribution.

The lifetimes are determined with unbinned maximum- likelihood fits to the ðt;σtÞ distributions of the candidates populating the signal regions. Each signal probability- density function (PDF) is the convolution of an exponential distribution intwith a resolution function that depends on σt, multiplied by the PDF ofσt. In theD^þcase, simulation shows that a Gaussian distribution is sufficient to model the resolution function. The mean of the resolution function is allowed to float in the fit to account for a possible bias in the determination of the decay time; the width is the per- candidateσtscaled by a free parametersto account for a possible misestimation of the decay-time uncertainty. The fit returnss≈1.12(1.29) for theD⁰(D^þ) sample. In theD⁰ case, an additional Gaussian distribution is needed to describe the 3% of candidates with poorer resolution.

This second component shares its mean with the principal component but has its own free scaling parameter (s⁰≈2.5) for the broader width.

In theD⁰case, the signal region contains a 0.2% fraction of background candidates. Sensitivity to the background contamination and its effects on the decay-time distribution is very limited. For the sake of simplicity, the background is neglected in the fit and a systematic uncertainty is later assigned. In theD^þcase, the signal region contains a non- negligible amount of background, which is accounted for in the fit. The background is modeled using data with mðK⁻π^þπ^þÞ in the sideband ½1.758;1.814∪

½1.936;1.992GeV=c² (Fig. 1), which is assumed to contain exclusively background candidates and be repre- sentative of the background in the signal region, as verified

in simulation. The background PDF consists of a zero- lifetime component and two exponential components, all convolved with a Gaussian resolution function having a free mean and a width corresponding to sσ_t. To better constrain the background parameters, a simultaneous fit to the candidates in the signal region and sideband is performed. The background fraction is Gaussian con- strained in the fit to ð8.780.05Þ%, as measured in the mðK⁻π^þπ^þÞ fit.

The PDF of σtis a histogram template derived directly from the data. In the fit to theD⁰ sample, the template is derived assuming that all candidates in the signal region are signal decays. In the fit to theD^þ sample, the template is derived from the candidates in the signal region by subtracting the scaled distribution of the sideband data.

The PDF ofσ_tfor the background is obtained directly from the sideband data.

The lifetime fits are tested on fully simulated data and on sets of data generated by randomly sampling the PDF with parameters fixed to the values found in the fits to the data.

All tests yield unbiased results and expected parameter uncertainties, independent of the assumed values of theD⁰ andD^þ lifetimes.

The decay-time distributions of the data, with fit pro- jections overlaid, are shown in Fig. 2. The measured D⁰ and D^þ lifetimes 410.51.1ðstatÞ 0.8ðsystÞfs and 1030.44.7ðstatÞ 3.1ðsystÞfs, respectively, are consis- tent with their world averages[7]. The systematic uncer- tainties arise from the sources listed in Table I and described below. The total systematic uncertainty is the sum in quadrature of the individual components.

2 0 2 4 6 8 10 12

Decay time [ps]

1 10 102

103

1 10 102

103

104 Belle II

= 72 fb1

L dt

Data Fit

Background

Candidates per 70 fs

FIG. 2. Decay-time distributions of (top) D⁰→K⁻π^þ and (bottom) D^þ→K⁻π^þπ^þ candidates in their respective signal regions with fit projections overlaid.

The decay time and decay-time uncertainty are observed to be correlated in data and simulation reproduces these effects well. The dominant effect is that small σ_t values correspond to larger true decay times (and vice versa).

These correlations, when neglected in the fits, result in an imperfect description of thetdistribution as a function of σ_t. To quantify the impact on the results, our model that neglects the correlations is fit to 1000 samples of signal- only simulated decays, each the same size as the data. The samples are obtained by resampling, with repetition, a set of simulatede^þe⁻collisions corresponding to an integrated luminosity of500fb⁻¹. Upper bounds of 0.16 and 0.39 fs on the average absolute deviations of the measured life- times from their true values are derived and assigned as the systematic uncertainty due to the imperfect resolution model for the D⁰→K⁻π^þ and D^þ →K⁻π^þπ^þ cases, respectively. For signal decays, the bias of the decay-time resolution function depends nearly linearly on the candi- date mass and may not average out when the mass range is restricted. Varying the boundaries of the signal region shows that such a correlation has a negligible effect upon the measured lifetimes.

The background neglected in theD⁰→K⁻π^þ fit could result in a systematic bias on the measured lifetime. To estimate the size of the bias, we fit our model that neglects the background to 500 resampled sets of simulated e^þe⁻ collisions, each having the same size and signal-to- background proportion as the data. The measured lifetimes are corrected by subtracting the bias due to the neglectedt vsσ_tcorrelations. The average absolute difference between the resulting value and the simulated lifetime, 0.24 fs, is assigned as a systematic uncertainty due to the neglected background contamination in theD⁰→K⁻π^þ fit.

The background contamination under the D^þ→ K⁻π^þπ^þ peak is already accounted for in the fit of the D^þ lifetime using sideband data. In simulation, the side- band ðt;σtÞ distribution describes the background ðt;σtÞ distribution in the signal region well. The same might not hold in data given that some disagreement is observed between data and simulation in the t distribution of the candidates populating the sideband. We fit to one thousand samples of simulated data obtained by sampling the fit PDF for the signal region and by resampling from the simulated e^þe⁻ collisions for the sideband. The resulting samples feature sideband data that differ from the background in the

signal region with the same level of disagreement as observed between data and simulation. The absolute average difference between the measured and simulated lifetimes, 2.52 fs, is assigned as a systematic uncertainty due to the modeling of the backgroundðt;σtÞdistribution.

In the lifetime fit, the fraction of background candidates in the signal region is constrained from the fit to the mðK⁻π^þπ^þÞ distribution. When we change this back- ground fraction to values obtained from fitting to the mðK⁻π^þπ^þÞdistribution with alternative signal and back- ground PDFs, the change in the measured lifetime is negligible.

During data taking, a periodic calibration determines the alignments and surface deformations of the internal com- ponents of the PXD and SVD and the relative alignments of the PXD, SVD, and CDC using e^þe⁻ -collision, beam- background, and cosmic-ray events[26]. Unaccounted-for misalignment can bias the measurement of the charmed decay lengths and hence their decay times. Two sources of uncertainties associated with the alignment procedure are considered: the statistical precision and a possible system- atic bias. Their effects are evaluated using simulated signal- only decays reconstructed with a misaligned detector.

For the statistical contribution, we consider configurations derived from comparison of alignment parameters deter- mined from data acquired on two consecutive days. These configurations have magnitudes of misalignment compa- rable to the alignment precision as observed in data averaged over a typical alignment period. For the system- atic contribution, we consider configurations derived from simulation studies in which coherent global deformations of the vertex detectors (e.g., radial expansion) are intro- duced [27]. These deformations have magnitudes, deter- mined by the most misaligned sensors, ranging from about 50 to 700μm. The alignment procedure determines the magnitude of these deformations within 4μm accuracy.

We consider configurations in which the CDC is perfectly aligned and configurations in which it is misaligned.

Possible effects on the determination of the IR are also introduced by using parameters measured on misaligned samples of simulatede^þe⁻ →μ^þμ⁻ events, to fully mimic the procedure used for real data. For each misalignment configuration, we fit to the reconstructed signal candidates and estimate the lifetime bias. We estimate the systematic uncertainty due to imperfect detector alignment as the sum in quadrature of the largest biases observed in each of the statistical and systematic contributions. The resulting uncertainties are 0.72 and 1.70 fs for D⁰→K⁻π^þ and D^þ→K⁻π^þπ^þ decays, respectively. The absolute length scale of the vertex detector is determined with a precision significantly better than 0.01% and contributes negligibly to the systematic uncertainty.

The measurement of momenta is calibrated with the peak positions of abundant charmed-, strange-, and bottom- hadron decays. Uncertainty in the scaling of the momenta TABLE I. Systematic uncertainties.

Source τðD⁰Þ[fs] τðD^þÞ[fs]

Resolution model 0.16 0.39

Backgrounds 0.24 2.52

Detector alignment 0.72 1.70

Momentum scale 0.19 0.48

Total 0.80 3.10

results in a systematic uncertainty in the lifetimes of 0.19 fs for D⁰ and 0.48 fs for D^þ. Uncertainties in the D⁰ and D^þ masses [7] contribute negligibly to the systematic uncertainty.

As a cross-check, a statistically independent measure- ment of theD⁰lifetime is performed using approximately 146×10³ D^þ →D⁰ð→K⁻π^þπ⁻π^þÞπ^þ decays recon- structed in data with criteria similar to those used for the D⁰→K⁻π^þ mode and a signal purity greater than 99%.

The resulting lifetime,408.81.2ðstatÞfs, agrees with the value determined from theD⁰→K⁻π^þ mode.

Finally, the internal consistency of the measurement is tested by repeating the full analysis on various subsets of the data, i.e., running periods and running conditions, charmed-meson momentum and flight direction, and D^þ or D⁻ candidates. We have also studied different selection criteria and sideband definitions. In all cases, the resulting changes in the lifetimes are insignificant.

In conclusion, the D⁰ and D^þ lifetimes are measured usinge^þe⁻→c¯cdata collected by the Belle II experiment corresponding to an integrated luminosity of72fb⁻¹. The results,

τðD⁰Þ ¼410.51.1 ðstatÞ 0.8ðsystÞ fs and ð1Þ τðD^þÞ ¼1030.44.7ðstatÞ 3.1 ðsystÞfs; ð2Þ are the world’s most precise to date and are consistent with previous measurements [7]. Assuming that all systematic uncertainties are fully correlated between the two mea- surements, except those due to the background contami- nation (assumed uncorrelated), the total correlation coefficient is 18%. The ratio of lifetimes is τðD^þÞ=τðD⁰Þ ¼2.5100.013ðstatÞ 0.007ðsystÞ. These results demonstrate the vertexing capabilities of the Belle II detector and confirm our understanding of systematic effects that impact future decay-time-dependent analyses of neutral-meson mixing and mixing-inducedCPviolation.

We thank the SuperKEKB group for the excellent operation of the accelerator; the KEK cryogenics group for the efficient operation of the solenoid; the KEK computer group for on-site computing support; and the raw-data centers at BNL, DESY, GridKa, IN2P3, and INFN for off-site computing support. This work was supported by the following funding sources: Science Committee of the Republic of Armenia Grant No. 20TTCG-1C010; Australian Research Council and research Grants No. DP180102629, No. DP170102389, No. DP170102204, No. DP150103061, No. FT130100303, No. FT130100018, and No. FT120100745; Austrian Federal Ministry of Education, Science and Research, Austrian Science Fund No. P 31361-N36, and Horizon 2020 ERC Starting Grant No. 947006 “InterLeptons”; Natural Sciences and Engineering Research Council of

Canada, Compute Canada and CANARIE; Chinese Academy of Sciences and research Grant No. QYZDJ- SSW-SLH011, National Natural Science Foundation of China and research Grants No. 11521505, No. 11575017, No. 11675166, No. 11761141009, No. 11705209, and No. 11975076, LiaoNing Revitalization Talents Program under Contract No. XLYC1807135, Shanghai Municipal Science and Technology Committee under Contract No. 19ZR1403000, Shanghai Pujiang Program under Grant No. 18PJ1401000, and the CAS Center for Excellence in Particle Physics (CCEPP); the Ministry of Education, Youth, and Sports of the Czech Republic under Contract No. LTT17020 and Charles University Grants No. SVV 260448 and No. GAUK 404316; European Research Council, Seventh Framework PIEF-GA-2013- 622527, Horizon 2020 ERC-Advanced Grants No. 267104 and No. 884719, Horizon 2020 ERC- Consolidator Grant No. 819127, Horizon 2020 Marie Sklodowska-Curie Grant Agreement No. 700525

“NIOBE,” and Horizon 2020 Marie Sklodowska-Curie RISE project JENNIFER2 Grant Agreement No. 822070 (European grants); L’Institut National de Physique Nucl´eaire et de Physique des Particules (IN2P3) du CNRS (France); BMBF, DFG, HGF, MPG, and AvH Foundation (Germany); Department of Atomic Energy under Project Identification No. RTI 4002 and Department of Science and Technology (India); Israel Science Foundation Grant No. 2476/17, U.S.-Israel Binational Science Foundation Grant No. 2016113, and Israel Ministry of Science Grant No. 3-16543;

Istituto Nazionale di Fisica Nucleare and the research grants BELLE2; Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research Grants No. 16H03968, No. 16H03993, No. 16H06492, No. 16K05323, No. 17H01133, No. 17H05405, No. 18K03621, No. 18H03710, No. 18H05226, No. 19H00682, No. 26220706, and No. 26400255, the National Institute of Informatics, and Science Information NETwork 5 (SINET5), and the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan; National Research Foundation (NRF) of Korea Grants No. 2016R1-D1A1B-01010135, No. 2016R1- D1A1B-02012900, No. 2018R1-A2B-3003643, No. 2018R1-A6A1A-06024970, No. 2018R1-D1A1B- 07047294, No. 2019K1-A3A7A-09033840, and No. 2019R1-I1A3A-01058933, Radiation Science Research Institute, Foreign Large-size Research Facility Application Supporting project, the Global Science Experimental Data Hub Center of the Korea Institute of Science and Technology Information and KREONET/

GLORIAD; Universiti Malaya RU grant, Akademi Sains Malaysia, and Ministry of Education Malaysia; Frontiers of Science Program Contracts No. FOINS-296, No. CB- 221329, No. CB-236394, No. CB-254409, and No. CB- 180023, and No. SEP-CINVESTAV research Grant

No. 237 (Mexico); the Polish Ministry of Science and Higher Education and the National Science Center; the Ministry of Science and Higher Education of the Russian Federation, Agreement No. 14.W03.31.0026, and the HSE University Basic Research Program, Moscow; University of Tabuk research Grants No. S-0256-1438 and No. S- 0280-1439 (Saudi Arabia); Slovenian Research Agency and research Grants No. J1-9124 and No. P1-0135;

Agencia Estatal de Investigacion, Spain Grants No. FPA2014-55613-P and No. FPA2017-84445-P, and No. CIDEGENT/2018/020 of Generalitat Valenciana;

Ministry of Science and Technology and research Grants No. MOST106-2112-M-002-005-MY3 and No. MOST107-2119-M-002-035-MY3, and the Ministry of Education (Taiwan); Thailand Center of Excellence in Physics; TUBITAK ULAKBIM (Turkey); National Research Foundation of Ukraine, Project No. 2020.02/

0257, and Ministry of Education and Science of Ukraine;

the U.S. National Science Foundation and research Grants No. PHY-1807007 and No. PHY-1913789, and the U.S.

Department of Energy and research Awards No. DE-AC06- 76RLO1830, No. DE-SC0007983, No. DE-SC0009824, No. DE-SC0009973, No. DE-SC0010073, No. DE- SC0010118, No. DE-SC0010504, No. DE-SC0011784, No. DE-SC0012704, No. DE-SC0021274; and the Vietnam Academy of Science and Technology (VAST) under Grant No. DL0000.05/21-23.

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